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Theorem spimev 1955
Description: Distinct-variable version of spime 1950. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
spimev.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimev  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1626 . 2  |-  F/ x ph
2 spimev.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spime 1950 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1547
This theorem is referenced by:  speiv  2035  axsep  4271  dtru  4332  zfpair  4343  rlimdmafv  27711
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753  ax-12 1939
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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